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A005284
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Number of permutations by inversions.
(Formerly M4178)
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4
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1, 6, 27, 111, 440, 1717, 6655, 25728, 99412, 384320, 1487262, 5762643, 22357907, 86859412, 337879565, 1315952428, 5131231668, 20029728894, 78265410550, 306109412100, 1198306570554, 4694809541046, 18407850118383
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history;
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OFFSET
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6,2
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REFERENCES
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R. K. Guy, personal communication.
R. H. Moritz and R. C. Williams, A coin-tossing problem and some related combinatorics, Math. Mag., 61 (1988), 24-29.
E. Netto, Lehrbuch der Combinatorik. 2nd ed., Teubner, Leipzig, 1927, p. 96.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=6..28.
B. H. Margolius, Permutations with inversions, J. Integ. Seqs. Vol. 4 (2001), #01.2.4.
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FORMULA
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a(n)=2^{2n+5}/sqrt{pi n}Q(1+O(n^{-1})) where Q is a digital search tree constant, Q = 0.2887880951...
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MAPLE
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g := proc(n, k) option remember; if k=0 then return(1) else if (n=1 and k=1) then return(0) else if (k<0 or k>binomial(n, 2)) then return(0) else g(n-1, k)+g(n, k-1)-g(n-1, k-n) end if end if end if end proc; seq(g(j+6, j), j=0..30);
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CROSSREFS
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Cf. A008302, A005283, A005285.
Sequence in context: A216263 A003517 A108958 * A198694 A220101 A014825
Adjacent sequences: A005281 A005282 A005283 * A005285 A005286 A005287
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms, Maple code, asymptotic formula from Barbara Haas Margolius (margolius(AT)math.csuohio.edu) 5/31/01
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STATUS
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approved
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